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Let be the class of functions which are analytic in the unit disk . Let C(r) be the closed curve that is the image of the circle |z|=r < 1 under the mapping w = f(z), L(r) the length of C(r), and let A(r) be the area enclosed by the curve C(r). In 1968 D. K. Thomas shown that if , f is starlike with respect to the origin, and for 0≤r < 1, A(r) < A, an absolute constant, then Later, in 1969 Nunokawa has shown that if f is convex univalent, then This paper is devoted to obtaining a related correspondence between f(z) and L(r) for the case when f is univalent. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Gae sun Chung 《Journal of Applied Mathematics and Computing》1995,2(2):83-95
Given a closed subset of the familyS* (α) of functions starlike of order α, a continuous Fréchet differentiable functional,J, is constructed with this collection as the solution set to the extremal problem ReJ(f) overS* (α). The support points ofS* (α) is completely characterized and shown to coincide with the extreme points of its convex hulls. Given any finite collection of support points ofS* (α), a continuous linear functional,J, is constructed with this collection as the solution set to the extremal problem ReJ(f) overS* (α). 相似文献
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LetS denote the class of regular and univalent functions in |z|<1 with the normalizationf(0)=0,f′(0)=1. Denoted f=inf f∈s {|α||f(z)≠ α, |z|<1} and letS(d)={f¦f∈S,d f=d, 1/4≦d≦1}. The analytic functionf(z) is univalent in |z|<1 if and only if $$log\frac{{f(z) - f(\zeta )}}{{z - \zeta }} = \sum\limits_{m,n = 0}^\infty {d_{mn} z^m \zeta ^n } $$ converges in the bicylinder |z|<1, |ξ|<1. LetC mn =√mnd mn andC nn (d)= Max fεS(d){Re(C nn )}. The paper deals with the monotonicity ofc nn(d) and related functionals. 相似文献
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Summary A family, E, consisting of normalised univalent functions with univalent derivatives is studied with regard to the zeros of
these functions.
Entrata in Redazione il 29 marzo 1978. 相似文献
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N. A. Lebedev 《Journal of Mathematical Sciences》1984,26(6):2299-2310
This paper is the original version of the author's survey, published in an abridged form in the Mathematical Encyclopedia (N. A. Lebedev, Univalent function, in: Mathematical Encyclopedia, Vol. 3, Moscow (1982), pp. 1163–1168).This paper of N. A. Lebedev, which opens the present collection, represents a more developed preliminary version of N. A. Lebedev's survey paper Univalent functions, published in Mathematical Encyclopedia. The paper is published with only insignificant modifications. By italic letters we have denoted the titles of the sections in the Mathematical Encyclopedia, directly related to this survey paper — Editors' remark.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 5–21, 1983. 相似文献
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V. V. Kozhevnikov 《Mathematical Notes》2007,81(1-2):213-221
In the paper, the construction of a variational method for univalent functions is suggested; this construction uses the factorization theorem. As a consequence, an analog of the Goluzin variational formula is obtained. 相似文献
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王晓瑛 《纯粹数学与应用数学》2006,22(3):289-293
首先就Mbius变换在几何函数论上应用时存在的两个误区予以讨论,指出其存在的问题与如何改正;其次明确地指出用Baernstein方法估计m次对称单叶函数之逆函数系数时的不足之处;最后就S ingh与Puri一文中的一个结果给以改正,并用Ruschew eyh的共轭方法得到该结果成立的最佳范围. 相似文献
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Henryka Siejka 《Israel Journal of Mathematics》1986,54(3):291-300
The class Σb is defined to consist of meromorphic univalent functionsH omitting a disc with the radiusb:H(z)=z+ Σ
0
∞
A
n
z
−n
,z>1,H(b)>b ∈ (0, 1). By aid of FitzGerald inequalities the inverse coefficients of odd Σb-functions are maximized. The result extends the corresponding estimation, due to Netanyahu and Schober, fromb=0 to the whole interval (0, 1).
The author wishes to express her gratitude to Professor O. Tammi for valuable discussions connected with the problem.
This work was supported by a grant from the Finnish Ministry of Education. 相似文献
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《Journal of Mathematical Analysis and Applications》1987,128(2):586-592
In this paper some new subclasses of Bazilevic functions are defined and it is shown that these classes are preserved under certain integral operators. 相似文献
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Thomas H. Foregger 《Linear and Multilinear Algebra》2013,61(4):377-385
We determine where a linear combination of elementary symmetric functions attains as maximum and minimum over a certain convex set in Rn . We also show that an inequality for elementary symmetric functions proposed by S. Pierce is true. 相似文献
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Thomas H. Foregger 《Linear and Multilinear Algebra》1987,20(4):377-385
We determine where a linear combination of elementary symmetric functions attains as maximum and minimum over a certain convex set in Rn. We also show that an inequality for elementary symmetric functions proposed by S. Pierce is true. 相似文献
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